Recent results of Bloomfield and Watson and Knott are used to derive a class of union-intersection tests for sphericity from likelihood ratio tests of independence of two sets of variates. It is shown that the ordinary likelihood ratio test for sphericity has a natural union-intersection interpretation. (Author/RC)

Standard errors for maximum likelihood estimates of factor loadings are expressed in terms of the inverse of an augmented information matrix. This formulation arises naturally by viewing the problem as one in constrained maximum likelihood estimation. The constraints correspond to the form of rotation used. Results are given for canonical rotation…

A group of factor analytic rotation procedures are developed which yield both hyperplane fittings and oblique Procrustean analyses as special cases. It is generally supposed that these techniques are rather different in approach. Illustrations are presented and discussed. (Author/JKS)

Gradient methods are employed in orthogonal oblique analytic rotation. Constraints are imposed on the elements of the transformation matrix by means of reparameterisations. (Author)

Two proposed methods of factor analyzing a correlation matrix using only the off-diagonal elements are compared. The purpose of these methods is to avoid using the diagonal communality elements which are generally unknown and must be estimated. (Author/JKS)

Two computer subroutine packages for the analytic rotation of a factor matrix, A(p x m), are described. The first program uses the Flectcher (1970) gradient method, and the second uses the Polak-Ribiere (Polak, 1971) gradient method. The calculations in both programs involve the optimization of a function of free parameters. The result is a…

Solutions for the indeterminate common factor of a group of variables satisfying the single common factor model are not unique. This paper examines a number of thereoms concerning that problem and draws conclusions from them for factor analysis in general. (Author/JKS)

Beginning with the results of Girschick on the asymptotic distribution of principal component loadings and those of Lawley on the distribution of unrotated maximum likelihood factor loadings, the asymptotic distributions of the corresponding analytically rotated loadings is obtained. The principal difficulty is the fact that the transformation…

A multiple time series is defined as the sum of an autoregressive process on a line and independent Gaussian white noise or a hyperplane that goes through the origin and intersects the line at a single point. This process is a multiple autoregressive time series in which the regression matrices satisfy suitable conditions. For a related article…

Outlined is a model for transformation of one factor matrix to congruence with a second or target matrix in which the correlations among the transformed factors are constrained to certain pre-specified values. Procedures are developed for implementing the model, and are illustrated with example factor solutions. (Author/RC)

Populations of factorially simple and complex data were generated with first the oblique and orthogonal factor models, and then solutions based on special cases of the general orthomax criterion were compared on the basis of these characteristics. The results are discussed and implications noted. (DEP)

Two population raw data matrices were constructed by computer simulation techniques. Each consisted of 10,000 subjects and 12 variables, and each was constructed according to an underlying factorial model consisting of four major common factors, eight minor common factors, and 12 unique factors. The computer simulation techniques were employed to…